What is the obligation of the mother in these two scenarios: a mother with three full-sibling sons, and a mother with a full-sister and a full-brother's son?

The mother's share in the first and second cases is one-third, due to the absence of a lineal descendant or a group of siblings. This is in accordance with the Almighty's saying: "And for his parents, each of them will have a sixth of what he left if he had a child" and "But if he had no child and his parents inherited him, then his mother will have a third." The children of brothers do not reduce the mother's share from one-third to one-sixth.